An involutive GVW algorithm and the computation of Pommaret bases

DOI10.1007/s11786-021-00512-5zbMath1505.13039OpenAlexW3156622747MaRDI QIDQ2051592

Daniel Robertz, Werner M. Seiler, Thomas Izgin, Amir Hashemi

Publication date: 24 November 2021

Published in: Mathematics in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11786-021-00512-5

zbMATH Keywords

Gröbner basesinvolutive basesPommaret basessignature-based algorithmsmodule of syzygiesGVW algorithmlinear coordinate transformationsquasi-stable position

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Uses Software

• Maple
• SyzInv.mpl

Cites Work

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• An improvement over the GVW algorithm for inhomogeneous polynomial systems
• Involution. The formal theory of differential equations and its applications in computer algebra
• A combinatorial approach to involution and \(\delta \)-regularity. II: Structure analysis of polynomial modules with Pommaret bases
• On an installation of Buchberger's algorithm
• Involutive bases of polynomial ideals
• Deterministic genericity for polynomial ideals
• Speeding up the GVW algorithm via a substituting method
• Computation of Pommaret bases using syzygies
• GVW algorithm over principal ideal domains
• A new incremental algorithm for computing Groebner bases
• A new framework for computing Gröbner bases

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